Depending on which camera, it usually has a 50/50 chance, if you shield the camera under your shirt and the rain is moderate, not storming, the camera might have a chance, but if you are caught in a "hurricane conditions" for a hour, obviously the camera will be ruined.

My advice (proven from my past experience):

1. Take out the battery and put it in a dry pocket
2. Move with your back leaned over slightly so you become the camera's shelter
3. Dry off the camera ASAP, and next time, get a storm jacket

Yeah, putting it under your shirt and leaning forward is quite protective. A few drops on the body will not kill your system. But in torrential rain...
If you're a dog-owner and know how to deal with doggy-poo you always have a little plastic bag handy. So comes rain, you know how to protect your valuable camera

In the case of the 350D/400D you can get water proof cases that you can even use UNDERWATER! I bet you can get them for other cameras as well though, I am considering getting one for when I go on holiday next year, get some photos of stuff out in a pedal-o